That would seem to be contradicted by In A Mirror Darkly and These Are the Voyages.

In A Mirror Darkly isn't necessarily inconsistent, because there's nothing saying that the U.S.S. Defiant from the Prime Timeline wasn't shunted to the past of the NuMirror Universe.

(This also presumes, which I do, that the Nu Timeline has it's own NuMirror Universe that is approximately the same "distance" across the quantum realities from the Nu Universe as the original Mirror Universe was from the Prime Universe.)

As to These Are The Voyages, that episode isn't part of my personal canon (as someone else cleverly put it here recently, Deanna Troi's holodeck fanfic isn't canon ), and Berman and Braga can eat a big bag of {censored}.